Lithography using quantum entangled particles

ABSTRACT

A system of etching using quantum entangled particles to get shorter interference fringes. An interferometer is used to obtain an interference fringe. N entangled photons are input to the interferometer. This reduces the distance between interference fringes by n, where again n is the number of entangled photons.

CROSS REFERENCE TO RELATED APPLICATIONS

This is a divisional of U.S. application Ser. No. 09/393,200 filed Sep.10, 1999, which claims the benefit of the U.S. Provisional ApplicationNo. 60/135,315, filed on May 20, 1999.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

The invention described herein was made in the performance of work undera NASA contract, and is subject to the provisions of Public Law 96-517(35 U.S.C. 202) in which the Contractor has elected to retain title.

FIELD OF INVENTION

The present application describes a technique of using quantum-entangledparticles, e.g. photons, for lithography for etching features on acomputer chip that are smaller than the wavelength of light used in theetching process, by some fraction related to the number of entangledparticles.

BACKGROUND

Quantum mechanics tells us that certain unobserved physical systems canhave odd behavior. A particle which is decoupled from its environmentand which has two possible states will not necessarily be in either ofthose states, until observed. Putting this in quantum mechanical terms,the particle is simultaneously in a “superposition” of both of thosestates. However, this only applies while the particle is in certainconditions—decoupled from its environment. Any attempt to actuallyobserve the particle couples the particle to its environment, and hencecauses the particle to default into one or the other of the eigenstatesof the observable operator.

This behavior is part of the superposition principle. The “superpositionprinciple” is illustrated by a famous hypothetical experiement, calledthe cat paradox, a cat in a box with a vial of poison. The vialcontaining the poison could equally likely be opened or not opened. Ifthe box/cat/poison is decoupled from its environment, then the catachieves a state where it is simultaneously dead and not dead. However,any attempt to observe the cat, causes the system to default to dead oralive.

The theory of quantum mechanics predicts that N particles can also existin such superposition states.

Lithography is a process of etching features on a substrate.Photolithography uses light to etch these features. Each spot can beetched, or not etched, to form a desired feature. In general, it isdesirable to make the features as small as possible.

In the prior art, called Classical Optical Interferometric Lithography,a lithographic pattern is etched on a photosensitive material using acombination of phase shifters, substrate rotators, and a Mach-Zehnder orother optical interferometer. The minimum sized feature that can beproduced in this fashion is on the order of one-quarter of the opticalwavelength [Brueck 98]. The only way to improve on this resolutionclassically is to decrease the physical wavelength of the light used inthe etching process.

This can come at a tremendous commercial expense. Optical sources andimaging elements are not readily available at very short wavelengths,such as hard UV or soft x ray.

SUMMARY

The present system uses a plurality of entangled particles, e.g.,photons, in a lithographic system to change the lithographic effect ofthe photons.

The multiple entangled photons can etch features whose size is similarto that which could only be achieved by using light having a wavelengththat is a small fraction of the actual light wavelength that is used.

In one disclosed embodiment, two entangled photons can be used a form aninterference pattern that is double the frequency, or half the size, ofthe actual optical frequency that is used. This operation goes againstthe established teaching and understanding in the art that thewavelength of the illuminating light forms a limit on the size offeatures that can be etched. Usually, these features could not be madesmaller than one-quarter or one-half of the wavelength of the light usedto carry out the etching.

The present system enables forming features that are smaller thanone-quarter of the wavelength of the light that is used, by somemultiple related to the number of entangled particles that are used.

The present system for quantum lithography uses an interferometer thatforms an interference pattern whose fringe spacing depends on both thenumber of entangled photons entering the device as well as theirwavelength. Multiple entangled photons are used within theinterferometer. These n entangled photons experience a phase shift thatis greater, by a factor of n, than the normal phase shift that would beexperienced by a single photon of the same wavelength in the samedevice. The changed phase shift forms a changed interference pattern inthe output to achieve a changed frequency of interference fringes. By sodoing, finer features can be etched.

An n-fold improvement in linear resolution is obtained by using nentangled particles, e.g. photons. A two dimensional lithographicoperation effectively squares the improvement to density (n²). As such,the entangled quantum lithography system makes it possible to etchfeatures, for example, that are 1 to 10 nanometers apart, usingradiation that has a wavelength λ, of 100 nanometers or more.

Another important use of this system is to retrofit an existing system.Interferometric lithography systems are already known and used. Thissystem makes it possible to re-use those existing lithographic systemsto obtain Better etching results. The established techniques ofimproving lithographic technology is by requiring owners to buy or buildtotally new semiconductor fabrication equipment that use shorterwavelength light. This system improves the resolved output of the sameequipment. This allows existing interferometric lithography equipment tobe effectively retrofitted.

Also, previous attempts to reduce feature size have used shorterwavelength light to reduce the feature size. That shorter wavelengthlight is always more energetic. Hence it can cause damage to thesubstrate.

In contrast, the present system reduces the etched feature size withoutrequiring more energetic particles.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects will now be described in detail with referenceto the accompanying drawings wherein:

FIG. 1 shows a basic block diagram of the present system;

FIG. 2 shows a photon down converter;

FIG. 3 shows a diagram of the result with corrected photons;

FIG. 4 shows a Mach-Zehnder interferometer.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present system replaces the classic “analog” optics of alithographic system that has new “digital” optics that use a number ofquantum-entangled particles, photons, electrons, atoms, or the like.This will obtain the increased resolution, and reduction of feature sizewithout shortening the physical wave-length. This system uses quantumentanglement effects to produce the same result as that previouslyobtained by using a shorter wavelength.

For example, if the uncorrelated classical stream of photons is replacedby sets of n entangled photons, then the interference pattern has theform (1+cos(2nΦ)) with Φ=kx being the phase shift in one arm of theinterferometer, and k=2π/λ being the wave number. consequently, the peakto peak distance in the interference pattern now becomes λ/(2n). This issubstantially smaller than the original peal to peak spacing of λ/2 and,in fact, increases the linear solution by a factor of n. So even thoughthe optical source and imaging is done with a relatively long wavelength(λ), the effective wavelength of the interference pattern is λ/n.Therefore, the resolution increases by a factor of n.

Analog classical optics operate according to the so-called Rayleighdiffraction limit which imposes a restriction on minimum feature sizethat can be etched by a photon or other particle. This minimum featuresize cannot be smaller than half a wavelength. The minimum size linesare on the order of λ/2, where λ is the optical wavelength used for theexposure. This limit on line sizes generally holds whenever classicaloptics and lenses are used for interferometric lithographic etching(Brueck 98).

Put mathematically, the prior art classical device lays down a series ofinterferometrically-produced lines which obey the function form1+cos(2Φ) where k=2π/λ is the wave number, and λ is the opticalwavelength, where I is the optical intensity and K=2II/λ is the wavenumber, and λ is the optical wavelength.

Quantum entangled photons are used in this application for reducing thesize of the features. In a classical stream of photons used forinterferometric lithography, the minimum size feature is on the order ofone-half the optical wavelength. For a stream of n entangled photons,the interference pattern has the form (1+cos(2nΦ)) with Φ=kx, andk=2π/λ, resulting in an effective resolution of the interference patternthat scales linearly with n. The size of the feature is a function ofthe number of entangled photons n. Thus, for a given wavelength ofphoton, the resolution for entangled photons increases by n over thenon-entangled classical system along one dimension. Etching in twodimensions can increase the resolution by n².

A single photon can be downconverted into two photons of lowerwavelength. The polarization, energy and position of the resulting twophotons are correlated because of conservation principles. In thisparticular case, the position correlation provides scaling properties.The ability to produce these entangled photons is well understood.

The present system uses particle beams which are quantum in nature tocarry out this operation. These beams are composed of streams of singlephotons, each of which is an individual quantum particle that isdecoupled from the system around it. The correlated particles are madeto behave in a way that is non-locally correlated. In accordance withquantum mechanical theory, the position, direction of motion, andfrequency of each photon depends on the other photon(s).

In the quantum optics community, it has been know for many years thatlight can exist in an entirely nonclassical state called a number stateor a Fock state. This is described by Scully. The number state has noclassical analog, as the coherent state does. In particular, the numberstate |N> has a precise and fixed number of photons in it. This is incontrast to the classical-like coherent state, which can only bedetermined to have a mean number of photons n_(mean)=|α|² due to thequantum fluctuation factor Δn. The number state |N> has no intensityfluctuations, ΔN=O. This is a remarkable fact that gives the numberstate a digital quality; one can have either 0, 1, 2, etc., photons in asingle number-state mode. Particles in number states can be produced enmasse by a process called parametric downconversion. Number states have,however, somewhat paradoxical and non-intuitive properties.

FIG. 1 shows a block diagram of the overall quantum lithographic etchingsystem. A single photon 101 of specified frequency is output from laser99. This photon is sent to a downconverter 100.

A downconverter of this type receives a high-frequency photon into anonlinear optical crystal of a material such as KTP. A nonlinearinteraction in the crystal generates a pair of daughter photons. If theoriginal photon has frequency ω and vector wave number κ, then thedaughter photons have the very same quantities, ω₁, ω₂, κ₁, κ₂. Theparticles obey the laws of conservation of energy and momentum in theform,

ω=ω₁+ω₂,  (1a)

κ=κ₁+κ₂,  (1b)

which entangles or correlates the photons in terms of energy and wavenumber. This correlation is the basis for many interesting experimentswhere the two daughter photons can be treated as number states inparticular photon modes in an interferometer.

The schematic for the down-conversion process is shown in FIG. 2.Incoming high frequency photons from the left are down-converted in anonlinear crystal and produce two daughter photons that are correlatedin both momentum and frequency. The vector wave number conservationcondition, Eq. (1b), is degenerate in azimuthal angle about the initialphoton propagation axis, generating a typically circular pattern ofphotons.

A typical spectral pattern is shown in FIG. 3. Choosing two pointsequidistant apart, as illustrated by the crosses in the FIG. 3,identifies by angular separation a particular down converted pair.

“Parametric” down conversion imposes the additional restriction thatω₁=ω₂ and k₁=k₂, which selects photon pairs symmetrically placed aboutthe center of the spectrum in FIG. 2. By choosing appropriate angulardeflections in the optics, these particular pairs can be captured.

The correlated photon particles are coupled through a coupler system 110to beam splitter 122. This (122) is the input beam splitter to a partialMach-Zehnder interferometer with beam splitter 122, mirrors 126 and 128and a phase shifter 130. The Interferometer produces parallel lines asits output. It has been demonstrated in Brueck, 98, “Interferometriclithograph _from Periodic Arrays to Arbitrary Patterns”, MicroelectronEng 42,: 145-148 March 1998, that etching a series of parallel lines canbe generalized in the lithographic domain into forming any desiredfeature.

The correlations between the photons are quantum in nature, and theangular relation allows selection of a particular photon moving in aparticular path, generating desired nonclassical number states of theform |N>.

A more detailed schematic of the Mach-Zehnder interferometer (MZI) isshown in FIG. 4. First and second correlated input photons 1 and 2 areinput to both ports A and B.

Neglecting losses in the interferometer for this discussion, if theinput optical intensity is some constant I₀, then for a classicalinterferometer—if all the input power enters from input port A—thesuperposition of C and D on the substrate will yield an interferencepattern in lithographic resist at grazing incidence given by,

I=I _(o)(1+cos2kx)

where, k=2π/λ is the optical wave number, and x is the path differencebetween the first path 400 and the second path 402.

This result turns out have the same functional form whether or not oneuses classical input light, quantum coherent (ordinary laser) inputlight, or number-state input light, provided one only uses the one upperinput port A.

However, if both input ports A and B are used, then the results aredifferent. In the case of dual-input-port entangled number states,(|N>|O>+|O>|N>)/2, such as those produced in parametric photon downconversion, then the functional form of the two-photon absorptionintensity changes to,

I=I _(o)(1+cos(2Nkx))  (3)

Where the correlated photons enter the two ports entangled N at a time.Note that the N-photon interference pattern in that case oscillates Ntimes as fast as before. Since the fringe intensity feature size Δxdetermined by the Rayleigh Criterion is given by the intensityminimum-to-maximum condition NκΔ=π, or equivalently Δx=λ/(2N), as notedabove. This is a factor of N below the usual limit of Δx=λ/2.

In particular, using correlated photon pairs (i.e., N=2) it is possibleto etch features on the order of size Δx=λ/4. With correlated photontriplets (i.e. N=3) it is possible to obtain features on the order ofΔx=λ/6, and so on. Hence, using light of wavelength λ=200 nm, featuresof size Δx=50 nm can be etched using a stream of photons correlated twoat a time (i.e., a stream of photons such that N=2).

The physics can be understood with reference to the case of N=2, forexample. If the photons were not entangled or correlated, then at thefirst beam splitter in FIG. 4 would have a 50—50 chance of each photontaking the upper or lower path, independent of each other. The twophotons behave independently, and in this case the result of Eq. (2) isobtained.

However, if the two input photons are entangled in number and position,which can be obtained from the down-conversion process using thedownconverter 100 of FIG. 2, then the entangled photon pair move as asingle unit. At the first beam splitter, both photons either take theupper path together, or they both take the lower path together. Quantummechanically, this is written as, $\begin{matrix}{\frac{{\Psi\rangle} = {{{2\rangle}_{L}{0\rangle}_{U}} + {{0\rangle}_{U}{2\rangle}_{U}}}}{\sqrt{2}},} & (4)\end{matrix}$

where a 2 represents a bi-photon in the upper or lower branch mode, andthe first state vector corresponds to one of the correlated photons, andthe second to the other. We say that the bi-photon state is entangled innumber and position. There are only two possibilities; they both takethe high road (the path via mirror 128 in FIG. 1), or they both take thelow road (the path via mirror 126 in FIG. 1). Since it is impossible todistinguish, even in principle, which of these possibilitiesoccurred-quantum mechanics demands that the probability amplitudesassociated with these two paths be added to create an interferencepattern.

Taking the phase differential Δφ=kx to be associated with an extradistance x in the upper path only, for convenience. Then afterpropagating across the MZI, the state now has the form, $\begin{matrix}\begin{matrix}{{{\Psi}\rangle} = \frac{{{2\rangle}_{L}{0\rangle}_{U}} + {{0\rangle}_{L}^{2\quad {kx}}{2\rangle}_{U}}}{\sqrt{2}}} \\{= \frac{{{2\rangle}_{L}{0\rangle}_{U}} + {^{2\quad {kx}}{0\rangle}_{L}{2\rangle}_{U}}}{\sqrt{2}}}\end{matrix} & (5)\end{matrix}$

where each photon in the correlated pair contributes one factor of kxfor a total of 2kx phase shift. When the state is interfered andrecombined by focusing the photons on the substrate, the interferencepattern has the form of Eq. (3) with N=2. This gives physical insightinto how this sub-wavelength diffraction comes about.

The physical mechanism for the sub-wavelength interference effect arisesthen from the quantum digital nature of entangled photons. The numberentanglement of the down-converted photon pair causes the photons to“talk” to each other in a nonlocal way. There is nothing at all likethis in classical theory, where there are no photons-only “analog”electromagnetic waves. In a sense, the correlated photon pair behaveslike a single entity, which is why it is referred to as a bi-photon.

This digital quantum mechanical object accumulates phase in theinterferometer in a very nonstandard fashion. In particular, since bothphotons in the di-photon pair take the same interferometer pathtogether, this object accumulates phase twice as fast as a single photonor a pair of un-entangled photons would. Since the phase shift isproportional to the path difference divided by the wavelength, and thewavelength is fixed, this means that the same path differential Δxprovides double the phase shift. This gives rise to two-photoninterference fringes that have half the spacing as before.

Interferometers have been used in lithography to produce an interferencepattern based on a phase shift that causes an interference pattern. FIG.1 shows a two-input port interferometer 120 whose output gives thedesired photon interference pattern. This is used to write an arbitrarypattern 142 on a Photographically sensitive material resist 145. This issimilar to the standard set up for state of the art classical opticalinterferometric lithography schemes. The present invention replaces theclassical electromagnetic fields with the appropriate quantum photoncreation and annihilation operators corresponding to the various ports.

According to the present system, the classical optical beam is replacedby a quantum stream of n entangled photons. We have shown that thismakes it possible to generate a simple linear matrix relationshipbetween the photon operators at the input ports and those at the outputports (Dowling 98). The details of the transfer matrix depends on theoptical elements that make up the interferometer. More phase shifters,beam splitters, mirrors, etc., make a more complex matrix. Nevertheless,it is still linear and it is a straightforward problem to translate anyarbitrary two-port interferometric system into an appropriate two-by-twotransfer matrix. This matrix, can also include complex terms thataccount for noise sources in the interferometer. These noise sourcescould otherwise lead to photon loss or the loss of the quantumcorrelations.

One can think of the entire interferometer as a simple quantum circuitwith two inputs and two outputs. This allows the interferometer to behandled in the recently well-developed formalism of quantum circuittheory. Additional photon circuits can be added in parallel to thelithographic circuit in order to apply fault-tolerant quantum errorcorrection techniques in order to minimize the effect of noise sources,allowing maximum resolution and contrast in the lithographic exposure.

Once the quantum operator transfer matrix is in place, a completedescription of how an arbitrary photon state propagates through theinterferometer and images interferometric lines at the output portsexists. Now an additional degree of freedom is obtained by the widerange of photon input states. For example, choosing a coherent state inonly one input port gives the standard classical results, which can thenbe used as a control. Then combinations of number states for the quantuminput state can be used to image the sub-wavelength image at the output.The number of states can be chosen to be entangled or correlated in alarge number of different ways in the simulation. Some of these choicesare the natural output of a nonlinear photon down converter or aparametric oscillator, and others can be generated in preprocessing stepwith linear optical elements.

For example, it is well known that a simple optical beam splitter cantake an unentangled number direct-product state and convert it into anonseparable entangled number-state output, of the form of Eq. (4),needed for this device.

According to a first disclosed mode, correlated photon pairs (N=2) areused. This makes it possible to etch features on the order of sizex=λ/4. For example, light of wavelength 200 nanometers could be used toetch features of size x=50 nm using a stream of two entangled photonscorrelated photons. These photons are relatively easy to produce usingthe optical process of photon down conversion. Moreover, these photonsproduce the surface damage of a 200 nm photon, even though they have theresolution of a 100 nm photon.

Another mode uses correlated photon triplets (N=3). This etches featureson the order of x=λ/6 in three-photon absorption.

In fact, there is no theoretical limit on the number of correlatedphotons that could be produced, and hence no limit the amount ofdivision below the Rayleigh-limited value.

Another important advantage is beating the damage criterion that iscaused by etching in classical physics. Each photon carries an energye=hv which=hc/λ per photon. Hence the energy of the photons riseinversely with decreasing wavelengths.

This can cause undesired resist damage to the material being etched. Inaddition, statistical fluctuations, called shot noise, can causeclumping of the arriving high frequency photons and hence lead toirregularities in the etch. This system allows etching features thathave a better resolution without correspondingly increasing the damagepotential.

Specifically classical systems have a linear ratio of energy (damagepotential) to feature size. The present system improves this ratio by afactor of the number of entangled particles.

The laser used herein is a titanium sapphire laser, producing an outputwave on the order of 100 to 200 nanometers. The optically nonlinearcrystal is a KDP crystal doped with LiIO₃.

Any kind of interferometer could be used. While the presentspecification describes a Mach Zehnder Interferometer, any other kindcan be used with these teachings.

Although only a few embodiments have been disclosed in detail above,those with ordinary skill in the art certainly understand thatmodifications are possible in the preferred embodiment and that suchmodifications are intended to be encompassed within the followingclaims.

What is claimed is:
 1. A lithography method, comprising: producing aplurality n of entangled particles; inputting said entangled particlesinto an interferometric device which produces a phase shift betweendifferent paths; and obtaining an output of said interferometric devicehaving a pattern spacing between parts of said pattern proportional to λover 4N where N is the number of entangled particles; and using saidoutput for lithography.
 2. A method as in claim 1 wherein said particlesare photons.
 3. A method as in claim 2 wherein there are two of saidphotons.
 4. A method as in claim 3 wherein there are three of saidphotons.
 5. A method of carrying out quantum lithography, comprising:obtaining a plurality of entangled particles, which are quantumentangled with one another; establishing an interferometer system whichis decoupled to its environment, and applying said entangled particlesinto said interferometer system to cause interference therebetween toform interference fringes spaced from one another by λ over 4N where Nis a number of decoupled photons; and using said interference fringe forlithography.
 6. A system, comprising: a lithographic system; and aplurality of entangled photons used in said lithographic system tochange a lithographic effect created by said lithographic system.
 7. Asystem as in claim 6, wherein said photons cause effects that can makesimilar line widths to that which could only be achieved by using alight having a wavelength that is a fraction of the actual lightwavelength that is used.
 8. A system as in claim 7, wherein there aretwo entangled photons that can be used to form a diffraction patternthat is double the frequency, or half the size, of the single photonpattern.
 9. A method of lithography, comprising; defining a desiredfeature size f; using an illuminating radiation for the lithography thathas an energy less than hc/λ, where λ is the wavelength used forclassical optical exposure of the features and f>λ/4; and etching saidspecified feature size using said less energetic photons.